• MA.5.AR.2 Algebraic Reasoning

Demonstrate an understanding of equality, the order of operations and equivalent numerical expressions

MA.5.AR.2.3

Determine and explain whether an equation involving any of the four operations is true or false. Example: The equation 2.5 + (6 × 2) = 16 − 1.5 can be determined to be true because the expression on both sides of the equal sign are equivalent to 14.5.

Benchmark Clarifications:
Clarification 1: Problem types include equations that include parenthesis but not nested parentheses.
Clarification 2: Instruction focuses on the connection between properties of equality and order of operations.

Purpose and Instructional Strategies
The purpose of this benchmark is to determine if students can connect their understanding of using the four operations reliably or fluently (MTR.3.1) to the concept of the meaning of the equal sign. Students have evaluated whether equations are true or false since Grade 2. In Grade 5, additional expectations include non-whole numbers and parentheses. In Grade 6, students extend this work to involve negative numbers and inequalities (MA.6.AR.2.1).

 Students will use their understanding of order of operations (MA.5.AR.2.2) to simplify expressions on each side of an equation (MTR.5.1).

 Students will determine if the expression on the left of equal sign is equivalent to the expression to the right of the equal sign. If these expressions are equivalent, then the equation is true.

 Students may use comparative relational thinking, instead of solving, in order to determine if the equation is true or false (MTR.2.1, MTR.3.1, MTR.5.1).

Common Misconceptions or Errors

 Some students may not understand that the equal sign is a relational symbol showing expressions on both sides that are the same. While justifying whether equations are true or false, students should explain what makes the equation true.

Using the numbers below, create an equation that is true. ( ___ × ___ ) − ____ = ____ − ____
12, 6.2, 5 1/5, 4, 3.5

Instructional Items
Instructional Item 1
Which best explains the equation below? 13.8 − 6 + 3 = 4 × 1.2
a. This equation is true because both sides of the equation are equal to 4.8.
b. This equation is true because both sides of the equation are equal to 10.8.
c. This equation is false because both sides of the equation are equal to 4.8.
d. This equation is false because both sides of the equation are unequal.

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